{"title":"Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff–Sagnotti counter-terms, and geometric flows","authors":"","doi":"10.1016/j.aop.2024.169812","DOIUrl":null,"url":null,"abstract":"<div><div>Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating quantum gravity, QG, argue that the asymptotic safety does not survive once certain perturbative terms (in general, nonassociative and noncommutative) are included in the projection space. The goal of this work is to prove that a generalized asymptotic safety scenario allows us to formulate physically viable nonassociative QG theories using effective models defined by generic off-diagonal solutions and nonlinear symmetries in nonassociative geometric flow and gravity theories. We elaborate on a new nonholonomic functional renormalization techniques with parametric renormalization group, RG, flow equations for effective actions supplemented by certain canonical two-loop counter-terms. The geometric constructions and quantum deformations are performed for nonassociative phase spaces modelled as R-flux deformed cotangent Lorentz bundles. Our results prove that theories involving nonassociative modifications of GR can be well defined both as classical nonassociative MGTs and QG models. Such theories are characterized by generalized G. Perelman thermodynamic variables which are computed for certain examples of nonassociative geometric and RG flows.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0003491624002197","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating quantum gravity, QG, argue that the asymptotic safety does not survive once certain perturbative terms (in general, nonassociative and noncommutative) are included in the projection space. The goal of this work is to prove that a generalized asymptotic safety scenario allows us to formulate physically viable nonassociative QG theories using effective models defined by generic off-diagonal solutions and nonlinear symmetries in nonassociative geometric flow and gravity theories. We elaborate on a new nonholonomic functional renormalization techniques with parametric renormalization group, RG, flow equations for effective actions supplemented by certain canonical two-loop counter-terms. The geometric constructions and quantum deformations are performed for nonassociative phase spaces modelled as R-flux deformed cotangent Lorentz bundles. Our results prove that theories involving nonassociative modifications of GR can be well defined both as classical nonassociative MGTs and QG models. Such theories are characterized by generalized G. Perelman thermodynamic variables which are computed for certain examples of nonassociative geometric and RG flows.
广义相对论(GR)的非共轭修正,由弦引力中具有 R 流变形的星积定义,是修正引力理论(MGT)的一个重要子类。长期以来,对量子引力(QG)的批评认为,一旦在投影空间中包含了某些微扰项(一般来说,非联立和非交换),其渐近安全性就不复存在了。这项工作的目标是证明广义渐近安全性方案允许我们利用非对偶几何流和引力理论中的通用非对偶解和非线性对称性定义的有效模型来提出物理上可行的非对偶 QG 理论。我们详细阐述了一种新的非荷尔蒙函数重正化技术,它具有参数重正化群(RG),有效作用的流动方程辅以某些典型的二环反条件。几何构造和量子变形是针对以 R 流变形余切洛伦兹束为模型的非耦合相空间进行的。我们的结果证明,涉及 GR 的非耦合修正的理论可以很好地定义为经典非耦合 MGT 和 QG 模型。这些理论由广义 G. 佩雷尔曼热力学变量表征,而这些变量是针对某些非耦合几何流和 RG 流的例子计算出来的。
期刊介绍:
Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance.
The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.